My question is what is the difference between +12v and -12v. Can anyone explain it with a practical example approach. 
can any one explain the real need of negative voltage(-9v). please try to explain in electron flow level, so as to get a clear idea. It's always confuses me. If question is repeated forgive Please. I want the real practical concept behind these supplies.
I think you are trying to view voltages as absolutes, the root of the negative voltage is the ground or the voltage reference. That is the place where you agree that the voltage is 0V we mostly interpret voltages as differences of potential, so as an exercise let's take your circuit and say that ground is not 0V but 20V so Vs is 29 and -Vs is 11. The difference of potential in both cases is 9 volts but relative to what reference is what decides the sign. If you make the gnd -9V then the voltage that was "negative" just becomes 0.
There is no change in what happens during electron flow, they will move from lower potential to higher potential as always(in most circuit books they write the current as going from high to low, but they are assuming protons move in this case, electron current is always the opposite direction)
you asked for a practical usage, the most practical one is that I can use one voltage(positive) to make it spin one way and negative to make it spin in the opposite direction. This is because I changed the direction of the current, but physically the same thing is happening, electrons are following the same rule.
remember that the ground being 0V is a convention we use for simplicity and this allows us to represent most voltages as a single number. However, a voltage is always a difference between two points and one doesn't always have to be 0.
To stop talking about voltages, you can just use height, let's say I am 6 feet tall and you are 7 feet tall, the difference is 1 feet either way, but if I use the smaller as the reference it is -1 and if I use the maximum as a reference it is 1.
Voltages are really only measured between two points. You can say that the voltage between points A and B is 12V, and the voltage between C and D is 9V.
But that becomes tiresome after a while. It makes life easier if you pick a point in the circuit, and declare that to be at 0V. By convention, the Earth is at 0V, but not all circuits are earthed. For a battery-powered circuit, you just pick a point of your choosing. That point is normally called "Ground" (or "Gnd" for short).
Having declared one point to be 0V, you can measure the voltage from there to any other point, and give the voltage at that point.
In the picture you added above, Ground is the point where the two batteries are connected. Which means that the positive terminal of the left battery must be at 9V.
The negative terminal of the right battery is 9V below it's positive terminal, and its positive terminal is at 0V. Which means the negative terminal must be at -9V.
If the negative terminal of the right battery was instead chosen as Ground, the voltages would instead be (from right to left) 0V, +9V and +18V.
The electrons don't care how we have chosen to label the voltages. Conventional current always flows from the more positive terminal to the more negative one. The electrons always flow from the more negative terminal to the more positive one.
One use for negative voltages is in audio power amplifiers. If you ground one terminal of a loudspeaker and connect a positive voltage to the other, the speaker cone moves one way. If you connect a negative voltage instead, the cone moves the other way. To get the full travel of the cone, you need to have both positive and negative voltages in your power supply. (Actually, a lot of small amplifiers just use a positive supply, and a capacitor, but for high-power amplifiers, having positive and negative power rails is better.)
